Reflections. These Coordinate Geometry questions are a great way for the ACT and SAT to assess not just your knowledge of transformations, but your understanding of slope and the equation of a line. Let’s look at what you need to know and then see how your skill set will be tested on the ACT and SAT.
A reflection occurs when an mirror image is created across a line of reflection. The test makers often use the x– and y-axes as the line of reflection. To understand how lines of reflection work, imagine holding a mirror on the line of reflection and glancing at the image in the mirror. Or you can imagine drawing the graphed equation with wet ink and folding the paper on the line of reflection.
If the x-axis is the line of reflection, place the mirror or fold on the x-axis:
y = –f(x) reflects y = f(x) across the x-axis
If the y-axis is the line of reflection, place the mirror or fold on the y-axis:
y = f(–x) reflects y = f(x) across the y-axis
The other two common lines of reflection are y = x and y = –x. Consider the following, in which the figure is reflected over y = x:
Now let’s examine how these concepts are tested on the ACT Math and SAT Math sections:
This question may be disconcerting because it doesn’t have a diagram to go with it. But that’s when you need to draw one.
This is considered a difficult question, but it’s made much easier with a diagram of line l and your knowledge of reflections. Need more ACT Math help? Check out our ACT courses.